Question: The sum of two angles is $88^\circ$. Angle 2 is $76^\circ$ smaller than $3$ times angle 1. What are the measures of the two angles in degrees?
Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 88}$ ${y = 3x-76}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${3x-76}$ for $y$ in the first equation. ${x + }{(3x-76)}{= 88}$ Simplify and solve for $x$ $ x+3x - 76 = 88 $ $ 4x-76 = 88 $ $ 4x = 164 $ $ x = \dfrac{164}{4} $ ${x = 41}$ Now that you know ${x = 41}$ , plug it back into $ {y = 3x-76}$ to find $y$ ${y = 3}{(41)}{ - 76}$ $y = 123 - 76$ ${y = 47}$ You can also plug ${x = 41}$ into $ {x+y = 88}$ and get the same answer for $y$ ${(41)}{ + y = 88}$ ${y = 47}$ The measure of angle 1 is $41^\circ$ and the measure of angle 2 is $47^\circ$.